Related papers: Noisy Random Boolean Formulae - a Statistical Phys…

We analyze the complexity of classically simulating continuous-time dynamics of locally interacting quantum spin systems with a constant rate of entanglement breaking noise. We prove that a polynomial time classical algorithm can be used to…

Variational quantum computing offers a powerful framework with applications across diverse fields such as quantum chemistry, machine learning, and optimization. However, its scalability is hindered by the exponential concentration of the…

We analyze changes in the thermodynamic properties of a spin system when it passes from the classical two-dimensional Ising model to the spin glass model, where spin-spin interactions are random in their values and signs. Formally, the…

A scheme to evaluate computation fidelities within the one-way model is developed and explored to understand the role of correlations in the quality of noisy quantum computations. The formalism is promptly applied to many computation…

Noisy monitored quantum circuits have emerged as a versatile and unifying framework connecting quantum many-body physics, quantum information, and quantum computation. In this review, we provide a comprehensive overview of recent advances…

The dynamical organization in the presence of noise of a Boolean neural network with random connections is analyzed. For low levels of noise, the system reaches a stationary state in which the majority of its elements acquire the same…

This paper resolves a pivotal open problem on nonparametric inference for nonlinear functionals of volatility matrix. Multiple prominent statistical tasks can be formulated as functionals of volatility matrix, yet a unified statistical…

Neural spikes in the brain form stochastic sequences, i.e., belong to the class of pulse noises. This stochasticity is a counterintuitive feature because extracting information - such as the commonly supposed neural information of mean…

Noise-based logic is a practically deterministic logic scheme inspired by the randomness of neural spikes and uses a system of uncorrelated stochastic processes and their superposition to represent the logic state. We briefly discuss…

Varied sensory systems use noise in order to enhance detection of weak signals. It has been conjectured in the literature that this effect, known as stochastic resonance, may take place in central cognitive processes such as the memory…

Understanding the boundary between classical simulatability and the power of quantum computation is a fascinating topic. Direct simulation of noisy quantum computation requires solving an open quantum many-body system, which is very costly.…

We show that scaling arguments are very useful to analyze the dynamics of periodically modulated noisy systems. Information about the behavior of the relevant quantities, such as the signal-to-noise ratio, upon variations of the noise…

Many qubit implementations are afflicted by correlated noise not captured by standard theoretical tools that are based on Markov approximations. While independent gate operations are a key concept for quantum computing, it is actually not…

Stochastic inverse problems considered in this article consist of estimating the probability distributions of intrinsically random inputs of computer models. These estimations are based on observable outputs affected by model noise, and…

Neuronal responses are conspicuously variable. We focus on one particular aspect of that variability: the precision of action potential timing. We show that for common models of noisy spike generation, elementary considerations imply that…

A new type of deterministic (non-probabilistic) computer logic system inspired by the stochasticity of brain signals is shown. The distinct values are represented by independent stochastic processes: independent voltage (or current) noises.…

We study Boolean circuits as a representation of Boolean functions and consider different equivalence, audit, and enumeration problems. For a number of restricted sets of gate types (bases) we obtain efficient algorithms, while for all…

A natural measure of smoothness of a Boolean function is its sensitivity (the largest number of Hamming neighbors of a point which differ from it in function value). The structure of smooth or equivalently low-sensitivity functions is still…

Analyzing the impact of noise is of fundamental importance to understand the advantages provided by quantum systems. While the classical simulability of noisy discrete-variable systems is increasingly well understood, noisy bosonic circuits…

This paper considers the problem of approximating a Boolean function $f$ using another Boolean function from a specified class. Two classes of approximating functions are considered: $k$-juntas, and linear Boolean functions. The $n$ input…